LMFDB - Embedded newform 8018.2.a.g.1.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8018,2,Mod(1,8018)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8018, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("8018.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8018 = 2 \cdot 19 \cdot 211 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8018.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$64.0240523407$
Analytic rank:	$1$
Dimension:	$34$
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.19
Character	$\chi$	$=$	8018.1

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +0.129131 q^{3} +1.00000 q^{4} -3.52572 q^{5} -0.129131 q^{6} -2.82586 q^{7} -1.00000 q^{8} -2.98333 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +0.129131 q^{3} +1.00000 q^{4} -3.52572 q^{5} -0.129131 q^{6} -2.82586 q^{7} -1.00000 q^{8} -2.98333 q^{9} +3.52572 q^{10} +3.84661 q^{11} +0.129131 q^{12} -4.00873 q^{13} +2.82586 q^{14} -0.455280 q^{15} +1.00000 q^{16} +0.713978 q^{17} +2.98333 q^{18} +1.00000 q^{19} -3.52572 q^{20} -0.364907 q^{21} -3.84661 q^{22} -5.48812 q^{23} -0.129131 q^{24} +7.43067 q^{25} +4.00873 q^{26} -0.772634 q^{27} -2.82586 q^{28} +2.59190 q^{29} +0.455280 q^{30} -1.63833 q^{31} -1.00000 q^{32} +0.496718 q^{33} -0.713978 q^{34} +9.96318 q^{35} -2.98333 q^{36} +3.57775 q^{37} -1.00000 q^{38} -0.517653 q^{39} +3.52572 q^{40} +9.15091 q^{41} +0.364907 q^{42} +7.97250 q^{43} +3.84661 q^{44} +10.5184 q^{45} +5.48812 q^{46} +0.365169 q^{47} +0.129131 q^{48} +0.985490 q^{49} -7.43067 q^{50} +0.0921969 q^{51} -4.00873 q^{52} -4.95620 q^{53} +0.772634 q^{54} -13.5621 q^{55} +2.82586 q^{56} +0.129131 q^{57} -2.59190 q^{58} +2.96434 q^{59} -0.455280 q^{60} +4.10222 q^{61} +1.63833 q^{62} +8.43046 q^{63} +1.00000 q^{64} +14.1336 q^{65} -0.496718 q^{66} +8.18705 q^{67} +0.713978 q^{68} -0.708688 q^{69} -9.96318 q^{70} +4.50465 q^{71} +2.98333 q^{72} +1.05393 q^{73} -3.57775 q^{74} +0.959531 q^{75} +1.00000 q^{76} -10.8700 q^{77} +0.517653 q^{78} -4.80776 q^{79} -3.52572 q^{80} +8.85020 q^{81} -9.15091 q^{82} +1.95637 q^{83} -0.364907 q^{84} -2.51728 q^{85} -7.97250 q^{86} +0.334696 q^{87} -3.84661 q^{88} -14.5954 q^{89} -10.5184 q^{90} +11.3281 q^{91} -5.48812 q^{92} -0.211559 q^{93} -0.365169 q^{94} -3.52572 q^{95} -0.129131 q^{96} +14.6473 q^{97} -0.985490 q^{98} -11.4757 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 34 q - 34 q^{2} - 6 q^{3} + 34 q^{4} + q^{5} + 6 q^{6} - 22 q^{7} - 34 q^{8} + 30 q^{9}+O(q^{10}) $ 34 * q - 34 * q^2 - 6 * q^3 + 34 * q^4 + q^5 + 6 * q^6 - 22 * q^7 - 34 * q^8 + 30 * q^9	\( 34 q - 34 q^{2} - 6 q^{3} + 34 q^{4} + q^{5} + 6 q^{6} - 22 q^{7} - 34 q^{8} + 30 q^{9} - q^{10} + 7 q^{11} - 6 q^{12} - 11 q^{13} + 22 q^{14} - 18 q^{15} + 34 q^{16} - 10 q^{17} - 30 q^{18} + 34 q^{19} + q^{20} + 14 q^{21} - 7 q^{22} - 30 q^{23} + 6 q^{24} + 11 q^{25} + 11 q^{26} - 21 q^{27} - 22 q^{28} + 12 q^{29} + 18 q^{30} - 13 q^{31} - 34 q^{32} - 4 q^{33} + 10 q^{34} - 16 q^{35} + 30 q^{36} - 46 q^{37} - 34 q^{38} - 36 q^{39} - q^{40} + 25 q^{41} - 14 q^{42} - 51 q^{43} + 7 q^{44} - 17 q^{45} + 30 q^{46} - 20 q^{47} - 6 q^{48} - 2 q^{49} - 11 q^{50} + 4 q^{51} - 11 q^{52} - 7 q^{53} + 21 q^{54} - 39 q^{55} + 22 q^{56} - 6 q^{57} - 12 q^{58} + 19 q^{59} - 18 q^{60} - 26 q^{61} + 13 q^{62} - 57 q^{63} + 34 q^{64} + 20 q^{65} + 4 q^{66} - 54 q^{67} - 10 q^{68} + 16 q^{70} + 9 q^{71} - 30 q^{72} - 57 q^{73} + 46 q^{74} + 26 q^{75} + 34 q^{76} + 2 q^{77} + 36 q^{78} - 7 q^{79} + q^{80} + 22 q^{81} - 25 q^{82} - 15 q^{83} + 14 q^{84} - 30 q^{85} + 51 q^{86} - 37 q^{87} - 7 q^{88} + 78 q^{89} + 17 q^{90} - 31 q^{91} - 30 q^{92} - 43 q^{93} + 20 q^{94} + q^{95} + 6 q^{96} - 38 q^{97} + 2 q^{98} + 2 q^{99}+O(q^{100}) \) 34 * q - 34 * q^2 - 6 * q^3 + 34 * q^4 + q^5 + 6 * q^6 - 22 * q^7 - 34 * q^8 + 30 * q^9 - q^10 + 7 * q^11 - 6 * q^12 - 11 * q^13 + 22 * q^14 - 18 * q^15 + 34 * q^16 - 10 * q^17 - 30 * q^18 + 34 * q^19 + q^20 + 14 * q^21 - 7 * q^22 - 30 * q^23 + 6 * q^24 + 11 * q^25 + 11 * q^26 - 21 * q^27 - 22 * q^28 + 12 * q^29 + 18 * q^30 - 13 * q^31 - 34 * q^32 - 4 * q^33 + 10 * q^34 - 16 * q^35 + 30 * q^36 - 46 * q^37 - 34 * q^38 - 36 * q^39 - q^40 + 25 * q^41 - 14 * q^42 - 51 * q^43 + 7 * q^44 - 17 * q^45 + 30 * q^46 - 20 * q^47 - 6 * q^48 - 2 * q^49 - 11 * q^50 + 4 * q^51 - 11 * q^52 - 7 * q^53 + 21 * q^54 - 39 * q^55 + 22 * q^56 - 6 * q^57 - 12 * q^58 + 19 * q^59 - 18 * q^60 - 26 * q^61 + 13 * q^62 - 57 * q^63 + 34 * q^64 + 20 * q^65 + 4 * q^66 - 54 * q^67 - 10 * q^68 + 16 * q^70 + 9 * q^71 - 30 * q^72 - 57 * q^73 + 46 * q^74 + 26 * q^75 + 34 * q^76 + 2 * q^77 + 36 * q^78 - 7 * q^79 + q^80 + 22 * q^81 - 25 * q^82 - 15 * q^83 + 14 * q^84 - 30 * q^85 + 51 * q^86 - 37 * q^87 - 7 * q^88 + 78 * q^89 + 17 * q^90 - 31 * q^91 - 30 * q^92 - 43 * q^93 + 20 * q^94 + q^95 + 6 * q^96 - 38 * q^97 + 2 * q^98 + 2 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	0.129131	0.0745539	0.0372770	−	0.999305i	$-0.488132\pi$
$3$	0.129131	0.0745539	0.0372770	+	0.999305i	$0.488132\pi$
$4$	1.00000	0.500000
$5$	−3.52572	−1.57675	−0.788374	−	0.615196i	$-0.789077\pi$
$5$	−3.52572	−1.57675	−0.788374	+	0.615196i	$0.789077\pi$
$6$	−0.129131	−0.0527176
$7$	−2.82586	−1.06808	−0.534038	−	0.845461i	$-0.679326\pi$
$7$	−2.82586	−1.06808	−0.534038	+	0.845461i	$0.679326\pi$
$8$	−1.00000	−0.353553
$9$	−2.98333	−0.994442
$10$	3.52572	1.11493
$11$	3.84661	1.15980	0.579898	−	0.814689i	$-0.303092\pi$
$11$	3.84661	1.15980	0.579898	+	0.814689i	$0.303092\pi$
$12$	0.129131	0.0372770
$13$	−4.00873	−1.11182	−0.555911	−	0.831242i	$-0.687631\pi$
$13$	−4.00873	−1.11182	−0.555911	+	0.831242i	$0.687631\pi$
$14$	2.82586	0.755243
$15$	−0.455280	−0.117553
$16$	1.00000	0.250000
$17$	0.713978	0.173165	0.0865825	−	0.996245i	$-0.472405\pi$
$17$	0.713978	0.173165	0.0865825	+	0.996245i	$0.472405\pi$
$18$	2.98333	0.703176
$19$	1.00000	0.229416
$19$	1.00000	0.229416
$20$	−3.52572	−0.788374
$21$	−0.364907	−0.0796292
$22$	−3.84661	−0.820100
$23$	−5.48812	−1.14435	−0.572176	−	0.820131i	$-0.693901\pi$
$23$	−5.48812	−1.14435	−0.572176	+	0.820131i	$0.693901\pi$
$24$	−0.129131	−0.0263588
$25$	7.43067	1.48613
$26$	4.00873	0.786177
$27$	−0.772634	−0.148694
$28$	−2.82586	−0.534038
$29$	2.59190	0.481304	0.240652	−	0.970611i	$-0.422639\pi$
$29$	2.59190	0.481304	0.240652	+	0.970611i	$0.422639\pi$
$30$	0.455280	0.0831224
$31$	−1.63833	−0.294253	−0.147126	−	0.989118i	$-0.547002\pi$
$31$	−1.63833	−0.294253	−0.147126	+	0.989118i	$0.547002\pi$
$32$	−1.00000	−0.176777
$33$	0.496718	0.0864674
$34$	−0.713978	−0.122446
$35$	9.96318	1.68408
$36$	−2.98333	−0.497221
$37$	3.57775	0.588179	0.294090	−	0.955778i	$-0.404984\pi$
$37$	3.57775	0.588179	0.294090	+	0.955778i	$0.404984\pi$
$38$	−1.00000	−0.162221
$39$	−0.517653	−0.0828907
$40$	3.52572	0.557465
$41$	9.15091	1.42913	0.714566	−	0.699568i	$-0.246624\pi$
$41$	9.15091	1.42913	0.714566	+	0.699568i	$0.246624\pi$
$42$	0.364907	0.0563064
$43$	7.97250	1.21580	0.607898	−	0.794015i	$-0.292013\pi$
$43$	7.97250	1.21580	0.607898	+	0.794015i	$0.292013\pi$
$44$	3.84661	0.579898
$45$	10.5184	1.56798
$46$	5.48812	0.809179
$47$	0.365169	0.0532654	0.0266327	−	0.999645i	$-0.491522\pi$
$47$	0.365169	0.0532654	0.0266327	+	0.999645i	$0.491522\pi$
$48$	0.129131	0.0186385
$49$	0.985490	0.140784
$50$	−7.43067	−1.05086
$51$	0.0921969	0.0129101
$52$	−4.00873	−0.555911
$53$	−4.95620	−0.680786	−0.340393	−	0.940283i	$-0.610560\pi$
$53$	−4.95620	−0.680786	−0.340393	+	0.940283i	$0.610560\pi$
$54$	0.772634	0.105142
$55$	−13.5621	−1.82871
$56$	2.82586	0.377622
$57$	0.129131	0.0171038
$58$	−2.59190	−0.340334
$59$	2.96434	0.385924	0.192962	−	0.981206i	$-0.438191\pi$
$59$	2.96434	0.385924	0.192962	+	0.981206i	$0.438191\pi$
$60$	−0.455280	−0.0587764
$61$	4.10222	0.525235	0.262617	−	0.964900i	$-0.415414\pi$
$61$	4.10222	0.525235	0.262617	+	0.964900i	$0.415414\pi$
$62$	1.63833	0.208068
$63$	8.43046	1.06214
$64$	1.00000	0.125000
$65$	14.1336	1.75306
$66$	−0.496718	−0.0611417
$67$	8.18705	1.00021	0.500104	−	0.865965i	$-0.333295\pi$
$67$	8.18705	1.00021	0.500104	+	0.865965i	$0.333295\pi$
$68$	0.713978	0.0865825
$69$	−0.708688	−0.0853160
$70$	−9.96318	−1.19083
$71$	4.50465	0.534603	0.267302	−	0.963613i	$-0.413868\pi$
$71$	4.50465	0.534603	0.267302	+	0.963613i	$0.413868\pi$
$72$	2.98333	0.351588
$73$	1.05393	0.123353	0.0616766	−	0.998096i	$-0.480355\pi$
$73$	1.05393	0.123353	0.0616766	+	0.998096i	$0.480355\pi$
$74$	−3.57775	−0.415905
$75$	0.959531	0.110797
$76$	1.00000	0.114708
$77$	−10.8700	−1.23875
$78$	0.517653	0.0586126
$79$	−4.80776	−0.540916	−0.270458	−	0.962732i	$-0.587175\pi$
$79$	−4.80776	−0.540916	−0.270458	+	0.962732i	$0.587175\pi$
$80$	−3.52572	−0.394187
$81$	8.85020	0.983356
$82$	−9.15091	−1.01055
$83$	1.95637	0.214740	0.107370	−	0.994219i	$-0.465757\pi$
$83$	1.95637	0.214740	0.107370	+	0.994219i	$0.465757\pi$
$84$	−0.364907	−0.0398146
$85$	−2.51728	−0.273038
$86$	−7.97250	−0.859697
$87$	0.334696	0.0358831
$88$	−3.84661	−0.410050
$89$	−14.5954	−1.54711	−0.773557	−	0.633727i	$-0.781524\pi$
$89$	−14.5954	−1.54711	−0.773557	+	0.633727i	$0.781524\pi$
$90$	−10.5184	−1.10873
$91$	11.3281	1.18751
$92$	−5.48812	−0.572176
$93$	−0.211559	−0.0219377
$94$	−0.365169	−0.0376643
$95$	−3.52572	−0.361731
$96$	−0.129131	−0.0131794
$97$	14.6473	1.48721	0.743603	−	0.668621i	$-0.233115\pi$
$97$	14.6473	1.48721	0.743603	+	0.668621i	$0.233115\pi$
$98$	−0.985490	−0.0995495
$99$	−11.4757	−1.15335
$100$	7.43067	0.743067
$101$	−7.72542	−0.768708	−0.384354	−	0.923186i	$-0.625576\pi$
$101$	−7.72542	−0.768708	−0.384354	+	0.923186i	$0.625576\pi$
$102$	−0.0921969	−0.00912885
$103$	−5.10829	−0.503335	−0.251667	−	0.967814i	$-0.580979\pi$
$103$	−5.10829	−0.503335	−0.251667	+	0.967814i	$0.580979\pi$
$104$	4.00873	0.393089
$105$	1.28656	0.125555
$106$	4.95620	0.481389
$107$	−11.9303	−1.15334	−0.576671	−	0.816977i	$-0.695648\pi$
$107$	−11.9303	−1.15334	−0.576671	+	0.816977i	$0.695648\pi$
$108$	−0.772634	−0.0743468
$109$	−15.7361	−1.50724	−0.753620	−	0.657310i	$-0.771694\pi$
$109$	−15.7361	−1.50724	−0.753620	+	0.657310i	$0.771694\pi$
$110$	13.5621	1.29309
$111$	0.462000	0.0438511
$112$	−2.82586	−0.267019
$113$	20.1252	1.89322	0.946611	−	0.322379i	$-0.104483\pi$
$113$	20.1252	1.89322	0.946611	+	0.322379i	$0.104483\pi$
$114$	−0.129131	−0.0120942
$115$	19.3495	1.80435
$116$	2.59190	0.240652
$117$	11.9594	1.10564
$118$	−2.96434	−0.272889
$119$	−2.01760	−0.184953
$120$	0.455280	0.0415612
$121$	3.79641	0.345128
$122$	−4.10222	−0.371397
$123$	1.18167	0.106547
$124$	−1.63833	−0.147126
$125$	−8.56985	−0.766510
$126$	−8.43046	−0.751045
$127$	5.49427	0.487538	0.243769	−	0.969833i	$-0.421616\pi$
$127$	5.49427	0.487538	0.243769	+	0.969833i	$0.421616\pi$
$128$	−1.00000	−0.0883883
$129$	1.02950	0.0906423
$130$	−14.1336	−1.23960
$131$	13.3007	1.16209	0.581045	−	0.813871i	$-0.302644\pi$
$131$	13.3007	1.16209	0.581045	+	0.813871i	$0.302644\pi$
$132$	0.496718	0.0432337
$133$	−2.82586	−0.245033
$134$	−8.18705	−0.707254
$135$	2.72409	0.234452
$136$	−0.713978	−0.0612231
$137$	−0.355939	−0.0304099	−0.0152050	−	0.999884i	$-0.504840\pi$
$137$	−0.355939	−0.0304099	−0.0152050	+	0.999884i	$0.504840\pi$
$138$	0.708688	0.0603275
$139$	16.5628	1.40484	0.702421	−	0.711762i	$-0.252102\pi$
$139$	16.5628	1.40484	0.702421	+	0.711762i	$0.252102\pi$
$140$	9.96318	0.842042
$141$	0.0471547	0.00397115
$142$	−4.50465	−0.378021
$143$	−15.4200	−1.28949
$144$	−2.98333	−0.248610
$145$	−9.13831	−0.758896
$146$	−1.05393	−0.0872240
$147$	0.127257	0.0104960
$148$	3.57775	0.294090
$149$	−1.38411	−0.113391	−0.0566953	−	0.998392i	$-0.518056\pi$
$149$	−1.38411	−0.113391	−0.0566953	+	0.998392i	$0.518056\pi$
$150$	−0.959531	−0.0783454
$151$	1.70126	0.138446	0.0692232	−	0.997601i	$-0.477948\pi$
$151$	1.70126	0.138446	0.0692232	+	0.997601i	$0.477948\pi$
$152$	−1.00000	−0.0811107
$153$	−2.13003	−0.172203
$154$	10.8700	0.875928
$155$	5.77628	0.463962
$156$	−0.517653	−0.0414454
$157$	−10.7668	−0.859286	−0.429643	−	0.902999i	$-0.641361\pi$
$157$	−10.7668	−0.859286	−0.429643	+	0.902999i	$0.641361\pi$
$158$	4.80776	0.382485
$159$	−0.640000	−0.0507553
$160$	3.52572	0.278732
$161$	15.5087	1.22225
$162$	−8.85020	−0.695338
$163$	−11.2583	−0.881818	−0.440909	−	0.897552i	$-0.645344\pi$
$163$	−11.2583	−0.881818	−0.440909	+	0.897552i	$0.645344\pi$
$164$	9.15091	0.714566
$165$	−1.75128	−0.136337
$166$	−1.95637	−0.151844
$167$	3.53119	0.273252	0.136626	−	0.990623i	$-0.456374\pi$
$167$	3.53119	0.273252	0.136626	+	0.990623i	$0.456374\pi$
$168$	0.364907	0.0281532
$169$	3.06993	0.236149
$170$	2.51728	0.193067
$171$	−2.98333	−0.228141
$172$	7.97250	0.607898
$173$	8.98455	0.683083	0.341541	−	0.939867i	$-0.389051\pi$
$173$	8.98455	0.683083	0.341541	+	0.939867i	$0.389051\pi$
$174$	−0.334696	−0.0253732
$175$	−20.9980	−1.58730
$176$	3.84661	0.289949
$177$	0.382788	0.0287721
$178$	14.5954	1.09397
$179$	−12.8588	−0.961109	−0.480554	−	0.876965i	$-0.659565\pi$
$179$	−12.8588	−0.961109	−0.480554	+	0.876965i	$0.659565\pi$
$180$	10.5184	0.783992
$181$	3.62297	0.269293	0.134647	−	0.990894i	$-0.457010\pi$
$181$	3.62297	0.269293	0.134647	+	0.990894i	$0.457010\pi$
$182$	−11.3281	−0.839696
$183$	0.529724	0.0391583
$184$	5.48812	0.404590
$185$	−12.6141	−0.927410
$186$	0.211559	0.0155123
$187$	2.74640	0.200836
$188$	0.365169	0.0266327
$189$	2.18336	0.158816
$190$	3.52572	0.255782
$191$	16.7083	1.20897	0.604486	−	0.796616i	$-0.293379\pi$
$191$	16.7083	1.20897	0.604486	+	0.796616i	$0.293379\pi$
$192$	0.129131	0.00931924
$193$	10.2059	0.734638	0.367319	−	0.930095i	$-0.380276\pi$
$193$	10.2059	0.734638	0.367319	+	0.930095i	$0.380276\pi$
$194$	−14.6473	−1.05161
$195$	1.82510	0.130698
$196$	0.985490	0.0703921
$197$	−22.6418	−1.61316	−0.806580	−	0.591124i	$-0.798684\pi$
$197$	−22.6418	−1.61316	−0.806580	+	0.591124i	$0.798684\pi$
$198$	11.4757	0.815542
$199$	4.59782	0.325931	0.162965	−	0.986632i	$-0.447894\pi$
$199$	4.59782	0.325931	0.162965	+	0.986632i	$0.447894\pi$
$200$	−7.43067	−0.525428
$201$	1.05720	0.0745694
$202$	7.72542	0.543559
$203$	−7.32436	−0.514069
$204$	0.0921969	0.00645507
$205$	−32.2635	−2.25338
$206$	5.10829	0.355911
$207$	16.3728	1.13799
$208$	−4.00873	−0.277956
$209$	3.84661	0.266076
$210$	−1.28656	−0.0887809
$211$	1.00000	0.0688428
$211$	1.00000	0.0688428
$212$	−4.95620	−0.340393
$213$	0.581690	0.0398568
$214$	11.9303	0.815535
$215$	−28.1088	−1.91700
$216$	0.772634	0.0525711
$217$	4.62969	0.314284
$218$	15.7361	1.06578
$219$	0.136095	0.00919648
$220$	−13.5621	−0.914353
$221$	−2.86215	−0.192529
$222$	−0.462000	−0.0310074
$223$	−22.1613	−1.48403	−0.742015	−	0.670383i	$-0.766130\pi$
$223$	−22.1613	−1.48403	−0.742015	+	0.670383i	$0.766130\pi$
$224$	2.82586	0.188811
$225$	−22.1681	−1.47787
$226$	−20.1252	−1.33871
$227$	0.535702	0.0355558	0.0177779	−	0.999842i	$-0.494341\pi$
$227$	0.535702	0.0355558	0.0177779	+	0.999842i	$0.494341\pi$
$228$	0.129131	0.00855192
$229$	−18.9075	−1.24945	−0.624723	−	0.780847i	$-0.714788\pi$
$229$	−18.9075	−1.24945	−0.624723	+	0.780847i	$0.714788\pi$
$230$	−19.3495	−1.27587
$231$	−1.40365	−0.0923537
$232$	−2.59190	−0.170167
$233$	0.257208	0.0168502	0.00842511	−	0.999965i	$-0.497318\pi$
$233$	0.257208	0.0168502	0.00842511	+	0.999965i	$0.497318\pi$
$234$	−11.9594	−0.781807
$235$	−1.28748	−0.0839861
$236$	2.96434	0.192962
$237$	−0.620833	−0.0403274
$238$	2.01760	0.130782
$239$	19.7654	1.27851	0.639257	−	0.768993i	$-0.279242\pi$
$239$	19.7654	1.27851	0.639257	+	0.768993i	$0.279242\pi$
$240$	−0.455280	−0.0293882
$241$	10.0743	0.648941	0.324470	−	0.945896i	$-0.394814\pi$
$241$	10.0743	0.648941	0.324470	+	0.945896i	$0.394814\pi$
$242$	−3.79641	−0.244043
$243$	3.46074	0.222007
$244$	4.10222	0.262617
$245$	−3.47456	−0.221981
$246$	−1.18167	−0.0753404
$247$	−4.00873	−0.255070
$248$	1.63833	0.104034
$249$	0.252629	0.0160097
$250$	8.56985	0.542005
$251$	21.1309	1.33377	0.666887	−	0.745159i	$-0.267627\pi$
$251$	21.1309	1.33377	0.666887	+	0.745159i	$0.267627\pi$
$252$	8.43046	0.531069
$253$	−21.1107	−1.32722
$254$	−5.49427	−0.344741
$255$	−0.325060	−0.0203560
$256$	1.00000	0.0625000
$257$	12.8967	0.804476	0.402238	−	0.915535i	$-0.368232\pi$
$257$	12.8967	0.804476	0.402238	+	0.915535i	$0.368232\pi$
$258$	−1.02950	−0.0640938
$259$	−10.1102	−0.628219
$260$	14.1336	0.876532
$261$	−7.73249	−0.478629
$262$	−13.3007	−0.821722
$263$	−11.6299	−0.717130	−0.358565	−	0.933505i	$-0.616734\pi$
$263$	−11.6299	−0.717130	−0.358565	+	0.933505i	$0.616734\pi$
$264$	−0.496718	−0.0305709
$265$	17.4741	1.07343
$266$	2.82586	0.173265
$267$	−1.88473	−0.115343
$268$	8.18705	0.500104
$269$	31.8016	1.93898	0.969490	−	0.245130i	$-0.0788308\pi$
$269$	31.8016	1.93898	0.969490	+	0.245130i	$0.0788308\pi$
$270$	−2.72409	−0.165783
$271$	8.46515	0.514221	0.257111	−	0.966382i	$-0.417230\pi$
$271$	8.46515	0.514221	0.257111	+	0.966382i	$0.417230\pi$
$272$	0.713978	0.0432913
$273$	1.46281	0.0885335
$274$	0.355939	0.0215030
$275$	28.5829	1.72361
$276$	−0.708688	−0.0426580
$277$	−3.87401	−0.232767	−0.116383	−	0.993204i	$-0.537130\pi$
$277$	−3.87401	−0.232767	−0.116383	+	0.993204i	$0.537130\pi$
$278$	−16.5628	−0.993373
$279$	4.88767	0.292617
$280$	−9.96318	−0.595414
$281$	−21.7024	−1.29466	−0.647328	−	0.762212i	$-0.724113\pi$
$281$	−21.7024	−1.29466	−0.647328	+	0.762212i	$0.724113\pi$
$282$	−0.0471547	−0.00280802
$283$	−16.6276	−0.988411	−0.494205	−	0.869345i	$-0.664541\pi$
$283$	−16.6276	−0.988411	−0.494205	+	0.869345i	$0.664541\pi$
$284$	4.50465	0.267302
$285$	−0.455280	−0.0269685
$286$	15.4200	0.911806
$287$	−25.8592	−1.52642
$288$	2.98333	0.175794
$289$	−16.4902	−0.970014
$290$	9.13831	0.536620
$291$	1.89142	0.110877
$292$	1.05393	0.0616766
$293$	−26.3670	−1.54038	−0.770190	−	0.637815i	$-0.779838\pi$
$293$	−26.3670	−1.54038	−0.770190	+	0.637815i	$0.779838\pi$
$294$	−0.127257	−0.00742181
$295$	−10.4514	−0.608504
$296$	−3.57775	−0.207953
$297$	−2.97202	−0.172454
$298$	1.38411	0.0801792
$299$	22.0004	1.27232
$300$	0.959531	0.0553986
$301$	−22.5292	−1.29856
$302$	−1.70126	−0.0978964
$303$	−0.997593	−0.0573102
$304$	1.00000	0.0573539
$305$	−14.4632	−0.828163
$306$	2.13003	0.121766
$307$	−19.0379	−1.08655	−0.543274	−	0.839555i	$-0.682816\pi$
$307$	−19.0379	−1.08655	−0.543274	+	0.839555i	$0.682816\pi$
$308$	−10.8700	−0.619375
$309$	−0.659639	−0.0375256
$310$	−5.77628	−0.328071
$311$	−6.44019	−0.365190	−0.182595	−	0.983188i	$-0.558450\pi$
$311$	−6.44019	−0.365190	−0.182595	+	0.983188i	$0.558450\pi$
$312$	0.517653	0.0293063
$313$	−29.6325	−1.67493	−0.837464	−	0.546493i	$-0.815962\pi$
$313$	−29.6325	−1.67493	−0.837464	+	0.546493i	$0.815962\pi$
$314$	10.7668	0.607607
$315$	−29.7234	−1.67472
$316$	−4.80776	−0.270458
$317$	−7.96203	−0.447192	−0.223596	−	0.974682i	$-0.571780\pi$
$317$	−7.96203	−0.447192	−0.223596	+	0.974682i	$0.571780\pi$
$318$	0.640000	0.0358894
$319$	9.97004	0.558215
$320$	−3.52572	−0.197093
$321$	−1.54057	−0.0859861
$322$	−15.5087	−0.864264
$323$	0.713978	0.0397268
$324$	8.85020	0.491678
$325$	−29.7876	−1.65232
$326$	11.2583	0.623540
$327$	−2.03202	−0.112371
$328$	−9.15091	−0.505274
$329$	−1.03192	−0.0568914
$330$	1.75128	0.0964050
$331$	−2.28660	−0.125683	−0.0628414	−	0.998024i	$-0.520016\pi$
$331$	−2.28660	−0.125683	−0.0628414	+	0.998024i	$0.520016\pi$
$332$	1.95637	0.107370
$333$	−10.6736	−0.584910
$334$	−3.53119	−0.193218
$335$	−28.8652	−1.57708
$336$	−0.364907	−0.0199073
$337$	−16.0881	−0.876376	−0.438188	−	0.898883i	$-0.644380\pi$
$337$	−16.0881	−0.876376	−0.438188	+	0.898883i	$0.644380\pi$
$338$	−3.06993	−0.166982
$339$	2.59879	0.141147
$340$	−2.51728	−0.136519
$341$	−6.30201	−0.341273
$342$	2.98333	0.161320
$343$	16.9962	0.917707
$344$	−7.97250	−0.429849
$345$	2.49863	0.134522
$346$	−8.98455	−0.483012
$347$	−6.96826	−0.374076	−0.187038	−	0.982353i	$-0.559889\pi$
$347$	−6.96826	−0.374076	−0.187038	+	0.982353i	$0.559889\pi$
$348$	0.334696	0.0179416
$349$	−15.9849	−0.855649	−0.427825	−	0.903862i	$-0.640720\pi$
$349$	−15.9849	−0.855649	−0.427825	+	0.903862i	$0.640720\pi$
$350$	20.9980	1.12239
$351$	3.09728	0.165321
$352$	−3.84661	−0.205025
$353$	−17.8106	−0.947962	−0.473981	−	0.880535i	$-0.657183\pi$
$353$	−17.8106	−0.947962	−0.473981	+	0.880535i	$0.657183\pi$
$354$	−0.382788	−0.0203450
$355$	−15.8821	−0.842934
$356$	−14.5954	−0.773557
$357$	−0.260535	−0.0137890
$358$	12.8588	0.679607
$359$	7.91721	0.417854	0.208927	−	0.977931i	$-0.433003\pi$
$359$	7.91721	0.417854	0.208927	+	0.977931i	$0.433003\pi$
$360$	−10.5184	−0.554366
$361$	1.00000	0.0526316
$362$	−3.62297	−0.190419
$363$	0.490235	0.0257307
$364$	11.3281	0.593755
$365$	−3.71586	−0.194497
$366$	−0.529724	−0.0276891
$367$	15.1357	0.790078	0.395039	−	0.918664i	$-0.370731\pi$
$367$	15.1357	0.790078	0.395039	+	0.918664i	$0.370731\pi$
$368$	−5.48812	−0.286088
$369$	−27.3001	−1.42119
$370$	12.6141	0.655778
$371$	14.0055	0.727131
$372$	−0.211559	−0.0109688
$373$	0.224885	0.0116441	0.00582205	−	0.999983i	$-0.498147\pi$
$373$	0.224885	0.0116441	0.00582205	+	0.999983i	$0.498147\pi$
$374$	−2.74640	−0.142013
$375$	−1.10663	−0.0571464
$376$	−0.365169	−0.0188322
$377$	−10.3902	−0.535125
$378$	−2.18336	−0.112300
$379$	−19.4967	−1.00148	−0.500738	−	0.865599i	$-0.666938\pi$
$379$	−19.4967	−1.00148	−0.500738	+	0.865599i	$0.666938\pi$
$380$	−3.52572	−0.180865
$381$	0.709482	0.0363479
$382$	−16.7083	−0.854872
$383$	7.43358	0.379838	0.189919	−	0.981800i	$-0.439177\pi$
$383$	7.43358	0.379838	0.189919	+	0.981800i	$0.439177\pi$
$384$	−0.129131	−0.00658970
$385$	38.3245	1.95320
$386$	−10.2059	−0.519467
$387$	−23.7846	−1.20904
$388$	14.6473	0.743603
$389$	26.5488	1.34608	0.673040	−	0.739606i	$-0.264988\pi$
$389$	26.5488	1.34608	0.673040	+	0.739606i	$0.264988\pi$
$390$	−1.82510	−0.0924173
$391$	−3.91840	−0.198162
$392$	−0.985490	−0.0497747
$393$	1.71754	0.0866384
$394$	22.6418	1.14068
$395$	16.9508	0.852888
$396$	−11.4757	−0.576675
$397$	3.43748	0.172522	0.0862612	−	0.996273i	$-0.472508\pi$
$397$	3.43748	0.172522	0.0862612	+	0.996273i	$0.472508\pi$
$398$	−4.59782	−0.230468
$399$	−0.364907	−0.0182682
$400$	7.43067	0.371533
$401$	−1.57879	−0.0788409	−0.0394205	−	0.999223i	$-0.512551\pi$
$401$	−1.57879	−0.0788409	−0.0394205	+	0.999223i	$0.512551\pi$
$402$	−1.05720	−0.0527285
$403$	6.56762	0.327157
$404$	−7.72542	−0.384354
$405$	−31.2033	−1.55050
$406$	7.32436	0.363502
$407$	13.7622	0.682168
$408$	−0.0921969	−0.00456442
$409$	−2.15926	−0.106769	−0.0533844	−	0.998574i	$-0.517001\pi$
$409$	−2.15926	−0.106769	−0.0533844	+	0.998574i	$0.517001\pi$
$410$	32.2635	1.59338
$411$	−0.0459628	−0.00226718
$412$	−5.10829	−0.251667
$413$	−8.37680	−0.412195
$414$	−16.3728	−0.804681
$415$	−6.89761	−0.338590
$416$	4.00873	0.196544
$417$	2.13878	0.104736
$418$	−3.84661	−0.188144
$419$	15.2124	0.743173	0.371587	−	0.928398i	$-0.378814\pi$
$419$	15.2124	0.743173	0.371587	+	0.928398i	$0.378814\pi$
$420$	1.28656	0.0627776
$421$	−28.0494	−1.36704	−0.683521	−	0.729931i	$-0.739552\pi$
$421$	−28.0494	−1.36704	−0.683521	+	0.729931i	$0.739552\pi$
$422$	−1.00000	−0.0486792
$423$	−1.08942	−0.0529693
$424$	4.95620	0.240694
$425$	5.30533	0.257346
$426$	−0.581690	−0.0281830
$427$	−11.5923	−0.560990
$428$	−11.9303	−0.576671
$429$	−1.99121	−0.0961364
$430$	28.1088	1.35553
$431$	4.23652	0.204066	0.102033	−	0.994781i	$-0.467465\pi$
$431$	4.23652	0.204066	0.102033	+	0.994781i	$0.467465\pi$
$432$	−0.772634	−0.0371734
$433$	−13.5588	−0.651595	−0.325798	−	0.945440i	$-0.605633\pi$
$433$	−13.5588	−0.651595	−0.325798	+	0.945440i	$0.605633\pi$
$434$	−4.62969	−0.222232
$435$	−1.18004	−0.0565787
$436$	−15.7361	−0.753620
$437$	−5.48812	−0.262532
$438$	−0.136095	−0.00650289
$439$	19.9634	0.952803	0.476401	−	0.879228i	$-0.341941\pi$
$439$	19.9634	0.952803	0.476401	+	0.879228i	$0.341941\pi$
$440$	13.5621	0.646546
$441$	−2.94004	−0.140002
$442$	2.86215	0.136138
$443$	−19.1349	−0.909126	−0.454563	−	0.890715i	$-0.650204\pi$
$443$	−19.1349	−0.909126	−0.454563	+	0.890715i	$0.650204\pi$
$444$	0.462000	0.0219255
$445$	51.4594	2.43941
$446$	22.1613	1.04937
$447$	−0.178731	−0.00845371
$448$	−2.82586	−0.133509
$449$	34.6768	1.63650	0.818249	−	0.574864i	$-0.194945\pi$
$449$	34.6768	1.63650	0.818249	+	0.574864i	$0.194945\pi$
$450$	22.1681	1.04501
$451$	35.2000	1.65750
$452$	20.1252	0.946611
$453$	0.219686	0.0103217
$454$	−0.535702	−0.0251417
$455$	−39.9397	−1.87240
$456$	−0.129131	−0.00604712
$457$	−22.8986	−1.07115	−0.535575	−	0.844488i	$-0.679905\pi$
$457$	−22.8986	−1.07115	−0.535575	+	0.844488i	$0.679905\pi$
$458$	18.9075	0.883491
$459$	−0.551644	−0.0257485
$460$	19.3495	0.902177
$461$	31.6534	1.47425	0.737124	−	0.675758i	$-0.236183\pi$
$461$	31.6534	1.47425	0.737124	+	0.675758i	$0.236183\pi$
$462$	1.40365	0.0653039
$463$	−15.5626	−0.723255	−0.361627	−	0.932323i	$-0.617779\pi$
$463$	−15.5626	−0.723255	−0.361627	+	0.932323i	$0.617779\pi$
$464$	2.59190	0.120326
$465$	0.745898	0.0345902
$466$	−0.257208	−0.0119149
$467$	27.5885	1.27664	0.638321	−	0.769770i	$-0.279629\pi$
$467$	27.5885	1.27664	0.638321	+	0.769770i	$0.279629\pi$
$468$	11.9594	0.552821
$469$	−23.1355	−1.06830
$470$	1.28748	0.0593871
$471$	−1.39033	−0.0640632
$472$	−2.96434	−0.136445
$473$	30.6671	1.41008
$474$	0.620833	0.0285158
$475$	7.43067	0.340942
$476$	−2.01760	−0.0924767
$477$	14.7860	0.677002
$478$	−19.7654	−0.904046
$479$	23.5236	1.07482	0.537411	−	0.843321i	$-0.319402\pi$
$479$	23.5236	1.07482	0.537411	+	0.843321i	$0.319402\pi$
$480$	0.455280	0.0207806
$481$	−14.3423	−0.653951
$482$	−10.0743	−0.458870
$483$	2.00265	0.0911238
$484$	3.79641	0.172564
$485$	−51.6422	−2.34495
$486$	−3.46074	−0.156982
$487$	−3.60682	−0.163441	−0.0817204	−	0.996655i	$-0.526041\pi$
$487$	−3.60682	−0.163441	−0.0817204	+	0.996655i	$0.526041\pi$
$488$	−4.10222	−0.185699
$489$	−1.45380	−0.0657430
$490$	3.47456	0.156964
$491$	−15.3856	−0.694344	−0.347172	−	0.937801i	$-0.612858\pi$
$491$	−15.3856	−0.694344	−0.347172	+	0.937801i	$0.612858\pi$
$492$	1.18167	0.0532737
$493$	1.85056	0.0833451
$494$	4.00873	0.180361
$495$	40.4600	1.81854
$496$	−1.63833	−0.0735631
$497$	−12.7295	−0.570996
$498$	−0.252629	−0.0113206
$499$	−6.75011	−0.302176	−0.151088	−	0.988520i	$-0.548278\pi$
$499$	−6.75011	−0.302176	−0.151088	+	0.988520i	$0.548278\pi$
$500$	−8.56985	−0.383255
$501$	0.455987	0.0203720
$502$	−21.1309	−0.943120
$503$	−3.33429	−0.148669	−0.0743343	−	0.997233i	$-0.523683\pi$
$503$	−3.33429	−0.148669	−0.0743343	+	0.997233i	$0.523683\pi$
$504$	−8.43046	−0.375523
$505$	27.2376	1.21206
$506$	21.1107	0.938483
$507$	0.396424	0.0176058
$508$	5.49427	0.243769
$509$	−1.39961	−0.0620365	−0.0310183	−	0.999519i	$-0.509875\pi$
$509$	−1.39961	−0.0620365	−0.0310183	+	0.999519i	$0.509875\pi$
$510$	0.325060	0.0143939
$511$	−2.97826	−0.131751
$512$	−1.00000	−0.0441942
$513$	−0.772634	−0.0341126
$514$	−12.8967	−0.568850
$515$	18.0104	0.793632
$516$	1.02950	0.0453212
$517$	1.40466	0.0617770
$518$	10.1102	0.444218
$519$	1.16019	0.0509265
$520$	−14.1336	−0.619802
$521$	12.0488	0.527866	0.263933	−	0.964541i	$-0.414980\pi$
$521$	12.0488	0.527866	0.263933	+	0.964541i	$0.414980\pi$
$522$	7.73249	0.338442
$523$	−26.1764	−1.14461	−0.572307	−	0.820039i	$-0.693951\pi$
$523$	−26.1764	−1.14461	−0.572307	+	0.820039i	$0.693951\pi$
$524$	13.3007	0.581045
$525$	−2.71150	−0.118340
$526$	11.6299	0.507087
$527$	−1.16973	−0.0509543
$528$	0.496718	0.0216169
$529$	7.11946	0.309542
$530$	−17.4741	−0.759028
$531$	−8.84358	−0.383779
$532$	−2.82586	−0.122517
$533$	−36.6835	−1.58894
$534$	1.88473	0.0815601
$535$	42.0627	1.81853
$536$	−8.18705	−0.353627
$537$	−1.66047	−0.0716545
$538$	−31.8016	−1.37107
$539$	3.79079	0.163281
$540$	2.72409	0.117226
$541$	−33.9186	−1.45827	−0.729137	−	0.684368i	$-0.760078\pi$
$541$	−33.9186	−1.45827	−0.729137	+	0.684368i	$0.760078\pi$
$542$	−8.46515	−0.363609
$543$	0.467839	0.0200769
$544$	−0.713978	−0.0306116
$545$	55.4808	2.37654
$546$	−1.46281	−0.0626027
$547$	−17.9165	−0.766054	−0.383027	−	0.923737i	$-0.625118\pi$
$547$	−17.9165	−0.766054	−0.383027	+	0.923737i	$0.625118\pi$
$548$	−0.355939	−0.0152050
$549$	−12.2382	−0.522315
$550$	−28.5829	−1.21878
$551$	2.59190	0.110419
$552$	0.708688	0.0301637
$553$	13.5861	0.577739
$554$	3.87401	0.164591
$555$	−1.62888	−0.0691421
$556$	16.5628	0.702421
$557$	24.2231	1.02637	0.513183	−	0.858279i	$-0.328466\pi$
$557$	24.2231	1.02637	0.513183	+	0.858279i	$0.328466\pi$
$558$	−4.88767	−0.206911
$559$	−31.9596	−1.35175
$560$	9.96318	0.421021
$561$	0.354645	0.0149731
$562$	21.7024	0.915460
$563$	22.4210	0.944934	0.472467	−	0.881348i	$-0.343364\pi$
$563$	22.4210	0.944934	0.472467	+	0.881348i	$0.343364\pi$
$564$	0.0471547	0.00198557
$565$	−70.9558	−2.98513
$566$	16.6276	0.698912
$567$	−25.0094	−1.05030
$568$	−4.50465	−0.189011
$569$	−34.5552	−1.44863	−0.724316	−	0.689469i	$-0.757844\pi$
$569$	−34.5552	−1.44863	−0.724316	+	0.689469i	$0.757844\pi$
$570$	0.455280	0.0190696
$571$	14.3172	0.599154	0.299577	−	0.954072i	$-0.403154\pi$
$571$	14.3172	0.599154	0.299577	+	0.954072i	$0.403154\pi$
$572$	−15.4200	−0.644744
$573$	2.15756	0.0901336
$574$	25.8592	1.07934
$575$	−40.7804	−1.70066
$576$	−2.98333	−0.124305
$577$	−27.8648	−1.16003	−0.580014	−	0.814606i	$-0.696953\pi$
$577$	−27.8648	−1.16003	−0.580014	+	0.814606i	$0.696953\pi$
$578$	16.4902	0.685903
$579$	1.31790	0.0547702
$580$	−9.13831	−0.379448
$581$	−5.52843	−0.229358
$582$	−1.89142	−0.0784020
$583$	−19.0646	−0.789574
$584$	−1.05393	−0.0436120
$585$	−42.1653	−1.74332
$586$	26.3670	1.08921
$587$	−41.5676	−1.71568	−0.857839	−	0.513919i	$-0.828193\pi$
$587$	−41.5676	−1.71568	−0.857839	+	0.513919i	$0.828193\pi$
$588$	0.127257	0.00524801
$589$	−1.63833	−0.0675062
$590$	10.4514	0.430278
$591$	−2.92376	−0.120267
$592$	3.57775	0.147045
$593$	−10.1211	−0.415624	−0.207812	−	0.978169i	$-0.566634\pi$
$593$	−10.1211	−0.415624	−0.207812	+	0.978169i	$0.566634\pi$
$594$	2.97202	0.121944
$595$	7.11349	0.291625
$596$	−1.38411	−0.0566953
$597$	0.593722	0.0242994
$598$	−22.0004	−0.899663
$599$	18.9960	0.776154	0.388077	−	0.921627i	$-0.373139\pi$
$599$	18.9960	0.776154	0.388077	+	0.921627i	$0.373139\pi$
$600$	−0.959531	−0.0391727
$601$	6.82489	0.278393	0.139197	−	0.990265i	$-0.455548\pi$
$601$	6.82489	0.278393	0.139197	+	0.990265i	$0.455548\pi$
$602$	22.5292	0.918221
$603$	−24.4246	−0.994648
$604$	1.70126	0.0692232
$605$	−13.3851	−0.544180
$606$	0.997593	0.0405244
$607$	−4.92248	−0.199797	−0.0998987	−	0.994998i	$-0.531852\pi$
$607$	−4.92248	−0.199797	−0.0998987	+	0.994998i	$0.531852\pi$
$608$	−1.00000	−0.0405554
$609$	−0.945803	−0.0383259
$610$	14.4632	0.585600
$611$	−1.46387	−0.0592217
$612$	−2.13003	−0.0861013
$613$	16.6533	0.672618	0.336309	−	0.941752i	$-0.390821\pi$
$613$	16.6533	0.672618	0.336309	+	0.941752i	$0.390821\pi$
$614$	19.0379	0.768306
$615$	−4.16622	−0.167998
$616$	10.8700	0.437964
$617$	33.3045	1.34079	0.670395	−	0.742004i	$-0.266125\pi$
$617$	33.3045	1.34079	0.670395	+	0.742004i	$0.266125\pi$
$618$	0.659639	0.0265346
$619$	27.2377	1.09477	0.547387	−	0.836879i	$-0.315623\pi$
$619$	27.2377	1.09477	0.547387	+	0.836879i	$0.315623\pi$
$620$	5.77628	0.231981
$621$	4.24031	0.170158
$622$	6.44019	0.258228
$623$	41.2447	1.65243
$624$	−0.517653	−0.0207227
$625$	−6.93851	−0.277540
$626$	29.6325	1.18435
$627$	0.496718	0.0198370
$628$	−10.7668	−0.429643
$629$	2.55444	0.101852
$630$	29.7234	1.18421
$631$	47.5555	1.89315	0.946577	−	0.322479i	$-0.104516\pi$
$631$	47.5555	1.89315	0.946577	+	0.322479i	$0.104516\pi$
$632$	4.80776	0.191243
$633$	0.129131	0.00513251
$634$	7.96203	0.316213
$635$	−19.3712	−0.768724
$636$	−0.640000	−0.0253777
$637$	−3.95056	−0.156527
$638$	−9.97004	−0.394718
$639$	−13.4388	−0.531632
$640$	3.52572	0.139366
$641$	−22.5914	−0.892307	−0.446154	−	0.894956i	$-0.647207\pi$
$641$	−22.5914	−0.892307	−0.446154	+	0.894956i	$0.647207\pi$
$642$	1.54057	0.0608014
$643$	25.6619	1.01201	0.506004	−	0.862531i	$-0.331122\pi$
$643$	25.6619	1.01201	0.506004	+	0.862531i	$0.331122\pi$
$644$	15.5087	0.611127
$645$	−3.62972	−0.142920
$646$	−0.713978	−0.0280911
$647$	−26.8513	−1.05563	−0.527817	−	0.849358i	$-0.676989\pi$
$647$	−26.8513	−1.05563	−0.527817	+	0.849358i	$0.676989\pi$
$648$	−8.85020	−0.347669
$649$	11.4026	0.447593
$650$	29.7876	1.16836
$651$	0.597837	0.0234311
$652$	−11.2583	−0.440909
$653$	−21.7992	−0.853068	−0.426534	−	0.904472i	$-0.640266\pi$
$653$	−21.7992	−0.853068	−0.426534	+	0.904472i	$0.640266\pi$
$654$	2.03202	0.0794581
$655$	−46.8946	−1.83232
$656$	9.15091	0.357283
$657$	−3.14422	−0.122668
$658$	1.03192	0.0402283
$659$	−31.8299	−1.23992	−0.619958	−	0.784635i	$-0.712850\pi$
$659$	−31.8299	−1.23992	−0.619958	+	0.784635i	$0.712850\pi$
$660$	−1.75128	−0.0681687
$661$	29.0452	1.12973	0.564865	−	0.825184i	$-0.308928\pi$
$661$	29.0452	1.12973	0.564865	+	0.825184i	$0.308928\pi$
$662$	2.28660	0.0888711
$663$	−0.369592	−0.0143538
$664$	−1.95637	−0.0759219
$665$	9.96318	0.386356
$666$	10.6736	0.413594
$667$	−14.2247	−0.550782
$668$	3.53119	0.136626
$669$	−2.86171	−0.110640
$670$	28.8652	1.11516
$671$	15.7796	0.609166
$672$	0.364907	0.0140766
$673$	−29.6444	−1.14271	−0.571353	−	0.820704i	$-0.693581\pi$
$673$	−29.6444	−1.14271	−0.571353	+	0.820704i	$0.693581\pi$
$674$	16.0881	0.619692
$675$	−5.74119	−0.220978
$676$	3.06993	0.118074
$677$	5.96020	0.229069	0.114534	−	0.993419i	$-0.463462\pi$
$677$	5.96020	0.229069	0.114534	+	0.993419i	$0.463462\pi$
$678$	−2.59879	−0.0998061
$679$	−41.3912	−1.58845
$680$	2.51728	0.0965334
$681$	0.0691759	0.00265083
$682$	6.30201	0.241317
$683$	18.3825	0.703387	0.351694	−	0.936115i	$-0.385606\pi$
$683$	18.3825	0.703387	0.351694	+	0.936115i	$0.385606\pi$
$684$	−2.98333	−0.114070
$685$	1.25494	0.0479487
$686$	−16.9962	−0.648917
$687$	−2.44155	−0.0931511
$688$	7.97250	0.303949
$689$	19.8681	0.756913
$690$	−2.49863	−0.0951212
$691$	−2.75060	−0.104638	−0.0523189	−	0.998630i	$-0.516661\pi$
$691$	−2.75060	−0.104638	−0.0523189	+	0.998630i	$0.516661\pi$
$692$	8.98455	0.341541
$693$	32.4287	1.23186
$694$	6.96826	0.264512
$695$	−58.3959	−2.21508
$696$	−0.334696	−0.0126866
$697$	6.53355	0.247476
$698$	15.9849	0.605036
$699$	0.0332135	0.00125625
$700$	−20.9980	−0.793651
$701$	−45.5981	−1.72222	−0.861109	−	0.508421i	$-0.830229\pi$
$701$	−45.5981	−1.72222	−0.861109	+	0.508421i	$0.830229\pi$
$702$	−3.09728	−0.116899
$703$	3.57775	0.134938
$704$	3.84661	0.144975
$705$	−0.166254	−0.00626150
$706$	17.8106	0.670310
$707$	21.8310	0.821038
$708$	0.382788	0.0143861
$709$	−3.66017	−0.137461	−0.0687303	−	0.997635i	$-0.521895\pi$
$709$	−3.66017	−0.137461	−0.0687303	+	0.997635i	$0.521895\pi$
$710$	15.8821	0.596045
$711$	14.3431	0.537909
$712$	14.5954	0.546987
$713$	8.99135	0.336729
$714$	0.260535	0.00975030
$715$	54.3666	2.03320
$716$	−12.8588	−0.480554
$717$	2.55233	0.0953183
$718$	−7.91721	−0.295468
$719$	21.2353	0.791942	0.395971	−	0.918263i	$-0.370408\pi$
$719$	21.2353	0.791942	0.395971	+	0.918263i	$0.370408\pi$
$720$	10.5184	0.391996
$721$	14.4353	0.537599
$722$	−1.00000	−0.0372161
$723$	1.30090	0.0483811
$724$	3.62297	0.134647
$725$	19.2596	0.715283
$726$	−0.490235	−0.0181943
$727$	39.0106	1.44682	0.723412	−	0.690417i	$-0.242573\pi$
$727$	39.0106	1.44682	0.723412	+	0.690417i	$0.242573\pi$
$728$	−11.3281	−0.419848
$729$	−26.1037	−0.966805
$730$	3.71586	0.137530
$731$	5.69219	0.210533
$732$	0.529724	0.0195792
$733$	1.40915	0.0520481	0.0260241	−	0.999661i	$-0.491715\pi$
$733$	1.40915	0.0520481	0.0260241	+	0.999661i	$0.491715\pi$
$734$	−15.1357	−0.558670
$735$	−0.448674	−0.0165496
$736$	5.48812	0.202295
$737$	31.4924	1.16004
$738$	27.3001	1.00493
$739$	−19.1821	−0.705624	−0.352812	−	0.935694i	$-0.614774\pi$
$739$	−19.1821	−0.705624	−0.352812	+	0.935694i	$0.614774\pi$
$740$	−12.6141	−0.463705
$741$	−0.517653	−0.0190164
$742$	−14.0055	−0.514159
$743$	−2.73289	−0.100260	−0.0501300	−	0.998743i	$-0.515964\pi$
$743$	−2.73289	−0.100260	−0.0501300	+	0.998743i	$0.515964\pi$
$744$	0.211559	0.00775614
$745$	4.87997	0.178788
$746$	−0.224885	−0.00823362
$747$	−5.83649	−0.213546
$748$	2.74640	0.100418
$749$	33.7132	1.23185
$750$	1.10663	0.0404086
$751$	−30.2698	−1.10456	−0.552281	−	0.833658i	$-0.686243\pi$
$751$	−30.2698	−1.10456	−0.552281	+	0.833658i	$0.686243\pi$
$752$	0.365169	0.0133163
$753$	2.72866	0.0994381
$754$	10.3902	0.378390
$755$	−5.99815	−0.218295
$756$	2.18336	0.0794079
$757$	44.9496	1.63372	0.816861	−	0.576835i	$-0.195712\pi$
$757$	44.9496	1.63372	0.816861	+	0.576835i	$0.195712\pi$
$758$	19.4967	0.708151
$759$	−2.72605	−0.0989492
$760$	3.52572	0.127891
$761$	−11.3650	−0.411981	−0.205991	−	0.978554i	$-0.566042\pi$
$761$	−11.3650	−0.411981	−0.205991	+	0.978554i	$0.566042\pi$
$762$	−0.709482	−0.0257018
$763$	44.4679	1.60985
$764$	16.7083	0.604486
$765$	7.50987	0.271520
$766$	−7.43358	−0.268586
$767$	−11.8832	−0.429079
$768$	0.129131	0.00465962
$769$	2.81664	0.101571	0.0507853	−	0.998710i	$-0.483828\pi$
$769$	2.81664	0.101571	0.0507853	+	0.998710i	$0.483828\pi$
$770$	−38.3245	−1.38112
$771$	1.66537	0.0599768
$772$	10.2059	0.367319
$773$	−22.2969	−0.801963	−0.400981	−	0.916086i	$-0.631331\pi$
$773$	−22.2969	−0.801963	−0.400981	+	0.916086i	$0.631331\pi$
$774$	23.7846	0.854919
$775$	−12.1739	−0.437299
$776$	−14.6473	−0.525807
$777$	−1.30555	−0.0468362
$778$	−26.5488	−0.951822
$779$	9.15091	0.327865
$780$	1.82510	0.0653489
$781$	17.3276	0.620031
$782$	3.91840	0.140122
$783$	−2.00259	−0.0715668
$784$	0.985490	0.0351961
$785$	37.9607	1.35488
$786$	−1.71754	−0.0612626
$787$	41.9480	1.49528	0.747642	−	0.664102i	$-0.231186\pi$
$787$	41.9480	1.49528	0.747642	+	0.664102i	$0.231186\pi$
$788$	−22.6418	−0.806580
$789$	−1.50178	−0.0534649
$790$	−16.9508	−0.603083
$791$	−56.8711	−2.02210
$792$	11.4757	0.407771
$793$	−16.4447	−0.583968
$794$	−3.43748	−0.121992
$795$	2.25646	0.0800283
$796$	4.59782	0.162965
$797$	−25.1575	−0.891123	−0.445562	−	0.895251i	$-0.646996\pi$
$797$	−25.1575	−0.891123	−0.445562	+	0.895251i	$0.646996\pi$
$798$	0.364907	0.0129176
$799$	0.260723	0.00922371
$800$	−7.43067	−0.262714
$801$	43.5430	1.53851
$802$	1.57879	0.0557489
$803$	4.05406	0.143065
$804$	1.05720	0.0372847
$805$	−54.6791	−1.92719
$806$	−6.56762	−0.231335
$807$	4.10658	0.144559
$808$	7.72542	0.271779
$809$	36.3537	1.27813	0.639064	−	0.769153i	$-0.279322\pi$
$809$	36.3537	1.27813	0.639064	+	0.769153i	$0.279322\pi$
$810$	31.2033	1.09637
$811$	−26.2537	−0.921892	−0.460946	−	0.887428i	$-0.652490\pi$
$811$	−26.2537	−0.921892	−0.460946	+	0.887428i	$0.652490\pi$
$812$	−7.32436	−0.257035
$813$	1.09312	0.0383372
$814$	−13.7622	−0.482366
$815$	39.6936	1.39041
$816$	0.0921969	0.00322754
$817$	7.97250	0.278923
$818$	2.15926	0.0754969
$819$	−33.7955	−1.18091
$820$	−32.2635	−1.12669
$821$	51.6694	1.80327	0.901637	−	0.432494i	$-0.142366\pi$
$821$	51.6694	1.80327	0.901637	+	0.432494i	$0.142366\pi$
$822$	0.0459628	0.00160314
$823$	15.9887	0.557332	0.278666	−	0.960388i	$-0.410108\pi$
$823$	15.9887	0.557332	0.278666	+	0.960388i	$0.410108\pi$
$824$	5.10829	0.177956
$825$	3.69094	0.128502
$826$	8.37680	0.291466
$827$	−7.28682	−0.253387	−0.126694	−	0.991942i	$-0.540437\pi$
$827$	−7.28682	−0.253387	−0.126694	+	0.991942i	$0.540437\pi$
$828$	16.3728	0.568996
$829$	−28.5782	−0.992562	−0.496281	−	0.868162i	$-0.665301\pi$
$829$	−28.5782	−0.992562	−0.496281	+	0.868162i	$0.665301\pi$
$830$	6.89761	0.239419
$831$	−0.500256	−0.0173537
$832$	−4.00873	−0.138978
$833$	0.703618	0.0243789
$834$	−2.13878	−0.0740599
$835$	−12.4500	−0.430849
$836$	3.84661	0.133038
$837$	1.26583	0.0437534
$838$	−15.2124	−0.525503
$839$	7.11379	0.245595	0.122798	−	0.992432i	$-0.460813\pi$
$839$	7.11379	0.245595	0.122798	+	0.992432i	$0.460813\pi$
$840$	−1.28656	−0.0443905
$841$	−22.2820	−0.768346
$842$	28.0494	0.966645
$843$	−2.80245	−0.0965217
$844$	1.00000	0.0344214
$845$	−10.8237	−0.372347
$846$	1.08942	0.0374550
$847$	−10.7281	−0.368623
$848$	−4.95620	−0.170197
$849$	−2.14715	−0.0736899
$850$	−5.30533	−0.181971
$851$	−19.6351	−0.673084
$852$	0.581690	0.0199284
$853$	−3.66432	−0.125464	−0.0627320	−	0.998030i	$-0.519981\pi$
$853$	−3.66432	−0.125464	−0.0627320	+	0.998030i	$0.519981\pi$
$854$	11.5923	0.396680
$855$	10.5184	0.359720
$856$	11.9303	0.407768
$857$	−37.4466	−1.27915	−0.639576	−	0.768728i	$-0.720890\pi$
$857$	−37.4466	−1.27915	−0.639576	+	0.768728i	$0.720890\pi$
$858$	1.99121	0.0679787
$859$	6.05528	0.206604	0.103302	−	0.994650i	$-0.467059\pi$
$859$	6.05528	0.206604	0.103302	+	0.994650i	$0.467059\pi$
$860$	−28.1088	−0.958501
$861$	−3.33923	−0.113801
$862$	−4.23652	−0.144296
$863$	−15.9280	−0.542194	−0.271097	−	0.962552i	$-0.587386\pi$
$863$	−15.9280	−0.542194	−0.271097	+	0.962552i	$0.587386\pi$
$864$	0.772634	0.0262855
$865$	−31.6770	−1.07705
$866$	13.5588	0.460747
$867$	−2.12940	−0.0723184
$868$	4.62969	0.157142
$869$	−18.4936	−0.627352
$870$	1.18004	0.0400072
$871$	−32.8197	−1.11205
$872$	15.7361	0.532890
$873$	−43.6976	−1.47894
$874$	5.48812	0.185638
$875$	24.2172	0.818690
$876$	0.136095	0.00459824
$877$	36.1942	1.22219	0.611095	−	0.791557i	$-0.290729\pi$
$877$	36.1942	1.22219	0.611095	+	0.791557i	$0.290729\pi$
$878$	−19.9634	−0.673733
$879$	−3.40481	−0.114841
$880$	−13.5621	−0.457177
$881$	−11.3724	−0.383144	−0.191572	−	0.981479i	$-0.561359\pi$
$881$	−11.3724	−0.383144	−0.191572	+	0.981479i	$0.561359\pi$
$882$	2.94004	0.0989961
$883$	9.26653	0.311843	0.155922	−	0.987769i	$-0.450165\pi$
$883$	9.26653	0.311843	0.155922	+	0.987769i	$0.450165\pi$
$884$	−2.86215	−0.0962644
$885$	−1.34960	−0.0453664
$886$	19.1349	0.642849
$887$	−39.2296	−1.31720	−0.658600	−	0.752493i	$-0.728851\pi$
$887$	−39.2296	−1.31720	−0.658600	+	0.752493i	$0.728851\pi$
$888$	−0.462000	−0.0155037
$889$	−15.5261	−0.520727
$890$	−51.4594	−1.72492
$891$	34.0433	1.14049
$892$	−22.1613	−0.742015
$893$	0.365169	0.0122199
$894$	0.178731	0.00597768
$895$	45.3363	1.51543
$896$	2.82586	0.0944054
$897$	2.84094	0.0948562
$898$	−34.6768	−1.15718
$899$	−4.24639	−0.141625
$900$	−22.1681	−0.738937
$901$	−3.53862	−0.117888
$902$	−35.2000	−1.17203
$903$	−2.90922	−0.0968128
$904$	−20.1252	−0.669355
$905$	−12.7736	−0.424608
$906$	−0.219686	−0.00729857
$907$	−56.9153	−1.88984	−0.944921	−	0.327299i	$-0.893862\pi$
$907$	−56.9153	−1.88984	−0.944921	+	0.327299i	$0.893862\pi$
$908$	0.535702	0.0177779
$909$	23.0474	0.764435
$910$	39.9397	1.32399
$911$	−12.7823	−0.423498	−0.211749	−	0.977324i	$-0.567916\pi$
$911$	−12.7823	−0.423498	−0.211749	+	0.977324i	$0.567916\pi$
$912$	0.129131	0.00427596
$913$	7.52540	0.249054
$914$	22.8986	0.757417
$915$	−1.86766	−0.0617428
$916$	−18.9075	−0.624723
$917$	−37.5860	−1.24120
$918$	0.551644	0.0182070
$919$	−33.8709	−1.11730	−0.558648	−	0.829405i	$-0.688680\pi$
$919$	−33.8709	−1.11730	−0.558648	+	0.829405i	$0.688680\pi$
$920$	−19.3495	−0.637936
$921$	−2.45838	−0.0810065
$922$	−31.6534	−1.04245
$923$	−18.0579	−0.594384
$924$	−1.40365	−0.0461768
$925$	26.5851	0.874113
$926$	15.5626	0.511418
$927$	15.2397	0.500537
$928$	−2.59190	−0.0850834
$929$	43.3130	1.42105	0.710527	−	0.703670i	$-0.248457\pi$
$929$	43.3130	1.42105	0.710527	+	0.703670i	$0.248457\pi$
$930$	−0.745898	−0.0244590
$931$	0.985490	0.0322981
$932$	0.257208	0.00842511
$933$	−0.831630	−0.0272263
$934$	−27.5885	−0.902722
$935$	−9.68301	−0.316668
$936$	−11.9594	−0.390904
$937$	−39.3283	−1.28480	−0.642400	−	0.766370i	$-0.722061\pi$
$937$	−39.3283	−1.28480	−0.642400	+	0.766370i	$0.722061\pi$
$938$	23.1355	0.755400
$939$	−3.82648	−0.124872
$940$	−1.28748	−0.0419930
$941$	28.2245	0.920094	0.460047	−	0.887895i	$-0.347833\pi$
$941$	28.2245	0.920094	0.460047	+	0.887895i	$0.347833\pi$
$942$	1.39033	0.0452995
$943$	−50.2213	−1.63543
$944$	2.96434	0.0964809
$945$	−7.69789	−0.250412
$946$	−30.6671	−0.997074
$947$	−9.68350	−0.314671	−0.157336	−	0.987545i	$-0.550290\pi$
$947$	−9.68350	−0.314671	−0.157336	+	0.987545i	$0.550290\pi$
$948$	−0.620833	−0.0201637
$949$	−4.22493	−0.137147
$950$	−7.43067	−0.241083
$951$	−1.02815	−0.0333399
$952$	2.01760	0.0653909
$953$	54.8832	1.77784	0.888920	−	0.458062i	$-0.151456\pi$
$953$	54.8832	1.77784	0.888920	+	0.458062i	$0.151456\pi$
$954$	−14.7860	−0.478713
$955$	−58.9088	−1.90624
$956$	19.7654	0.639257
$957$	1.28744	0.0416171
$958$	−23.5236	−0.760014
$959$	1.00583	0.0324801
$960$	−0.455280	−0.0146941
$961$	−28.3159	−0.913415
$962$	14.3423	0.462413
$963$	35.5918	1.14693
$964$	10.0743	0.324470
$965$	−35.9832	−1.15834
$966$	−2.00265	−0.0644343
$967$	8.34825	0.268462	0.134231	−	0.990950i	$-0.457144\pi$
$967$	8.34825	0.268462	0.134231	+	0.990950i	$0.457144\pi$
$968$	−3.79641	−0.122021
$969$	0.0921969	0.00296179
$970$	51.6422	1.65813
$971$	3.69003	0.118419	0.0592094	−	0.998246i	$-0.481142\pi$
$971$	3.69003	0.118419	0.0592094	+	0.998246i	$0.481142\pi$
$972$	3.46074	0.111003
$973$	−46.8043	−1.50048
$974$	3.60682	0.115570
$975$	−3.84650	−0.123187
$976$	4.10222	0.131309
$977$	−1.08237	−0.0346280	−0.0173140	−	0.999850i	$-0.505511\pi$
$977$	−1.08237	−0.0346280	−0.0173140	+	0.999850i	$0.505511\pi$
$978$	1.45380	0.0464873
$979$	−56.1430	−1.79434
$980$	−3.47456	−0.110991
$981$	46.9458	1.49886
$982$	15.3856	0.490975
$983$	−27.1041	−0.864487	−0.432243	−	0.901757i	$-0.642278\pi$
$983$	−27.1041	−0.864487	−0.432243	+	0.901757i	$0.642278\pi$
$984$	−1.18167	−0.0376702
$985$	79.8285	2.54355
$986$	−1.85056	−0.0589339
$987$	−0.133253	−0.00424148
$988$	−4.00873	−0.127535
$989$	−43.7540	−1.39130
$990$	−40.4600	−1.28590
$991$	13.3530	0.424172	0.212086	−	0.977251i	$-0.431974\pi$
$991$	13.3530	0.424172	0.212086	+	0.977251i	$0.431974\pi$
$992$	1.63833	0.0520170
$993$	−0.295271	−0.00937014
$994$	12.7295	0.403755
$995$	−16.2106	−0.513911
$996$	0.252629	0.00800484
$997$	−1.79399	−0.0568164	−0.0284082	−	0.999596i	$-0.509044\pi$
$997$	−1.79399	−0.0568164	−0.0284082	+	0.999596i	$0.509044\pi$
$998$	6.75011	0.213671
$999$	−2.76429	−0.0874584

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8018.2.a.g.1.19	✓	34

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8018.2.a.g.1.19	✓	34	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 8018 = 2 \cdot 19 \cdot 211 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8018.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +0.129131 q^{3} +1.00000 q^{4} -3.52572 q^{5} -0.129131 q^{6} -2.82586 q^{7} -1.00000 q^{8} -2.98333 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +0.129131 q^{3} +1.00000 q^{4} -3.52572 q^{5} -0.129131 q^{6} -2.82586 q^{7} -1.00000 q^{8} -2.98333 q^{9} +3.52572 q^{10} +3.84661 q^{11} +0.129131 q^{12} -4.00873 q^{13} +2.82586 q^{14} -0.455280 q^{15} +1.00000 q^{16} +0.713978 q^{17} +2.98333 q^{18} +1.00000 q^{19} -3.52572 q^{20} -0.364907 q^{21} -3.84661 q^{22} -5.48812 q^{23} -0.129131 q^{24} +7.43067 q^{25} +4.00873 q^{26} -0.772634 q^{27} -2.82586 q^{28} +2.59190 q^{29} +0.455280 q^{30} -1.63833 q^{31} -1.00000 q^{32} +0.496718 q^{33} -0.713978 q^{34} +9.96318 q^{35} -2.98333 q^{36} +3.57775 q^{37} -1.00000 q^{38} -0.517653 q^{39} +3.52572 q^{40} +9.15091 q^{41} +0.364907 q^{42} +7.97250 q^{43} +3.84661 q^{44} +10.5184 q^{45} +5.48812 q^{46} +0.365169 q^{47} +0.129131 q^{48} +0.985490 q^{49} -7.43067 q^{50} +0.0921969 q^{51} -4.00873 q^{52} -4.95620 q^{53} +0.772634 q^{54} -13.5621 q^{55} +2.82586 q^{56} +0.129131 q^{57} -2.59190 q^{58} +2.96434 q^{59} -0.455280 q^{60} +4.10222 q^{61} +1.63833 q^{62} +8.43046 q^{63} +1.00000 q^{64} +14.1336 q^{65} -0.496718 q^{66} +8.18705 q^{67} +0.713978 q^{68} -0.708688 q^{69} -9.96318 q^{70} +4.50465 q^{71} +2.98333 q^{72} +1.05393 q^{73} -3.57775 q^{74} +0.959531 q^{75} +1.00000 q^{76} -10.8700 q^{77} +0.517653 q^{78} -4.80776 q^{79} -3.52572 q^{80} +8.85020 q^{81} -9.15091 q^{82} +1.95637 q^{83} -0.364907 q^{84} -2.51728 q^{85} -7.97250 q^{86} +0.334696 q^{87} -3.84661 q^{88} -14.5954 q^{89} -10.5184 q^{90} +11.3281 q^{91} -5.48812 q^{92} -0.211559 q^{93} -0.365169 q^{94} -3.52572 q^{95} -0.129131 q^{96} +14.6473 q^{97} -0.985490 q^{98} -11.4757 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 34 q - 34 q^{2} - 6 q^{3} + 34 q^{4} + q^{5} + 6 q^{6} - 22 q^{7} - 34 q^{8} + 30 q^{9}+O(q^{10}) \) 34 * q - 34 * q^2 - 6 * q^3 + 34 * q^4 + q^5 + 6 * q^6 - 22 * q^7 - 34 * q^8 + 30 * q^9	\( 34 q - 34 q^{2} - 6 q^{3} + 34 q^{4} + q^{5} + 6 q^{6} - 22 q^{7} - 34 q^{8} + 30 q^{9} - q^{10} + 7 q^{11} - 6 q^{12} - 11 q^{13} + 22 q^{14} - 18 q^{15} + 34 q^{16} - 10 q^{17} - 30 q^{18} + 34 q^{19} + q^{20} + 14 q^{21} - 7 q^{22} - 30 q^{23} + 6 q^{24} + 11 q^{25} + 11 q^{26} - 21 q^{27} - 22 q^{28} + 12 q^{29} + 18 q^{30} - 13 q^{31} - 34 q^{32} - 4 q^{33} + 10 q^{34} - 16 q^{35} + 30 q^{36} - 46 q^{37} - 34 q^{38} - 36 q^{39} - q^{40} + 25 q^{41} - 14 q^{42} - 51 q^{43} + 7 q^{44} - 17 q^{45} + 30 q^{46} - 20 q^{47} - 6 q^{48} - 2 q^{49} - 11 q^{50} + 4 q^{51} - 11 q^{52} - 7 q^{53} + 21 q^{54} - 39 q^{55} + 22 q^{56} - 6 q^{57} - 12 q^{58} + 19 q^{59} - 18 q^{60} - 26 q^{61} + 13 q^{62} - 57 q^{63} + 34 q^{64} + 20 q^{65} + 4 q^{66} - 54 q^{67} - 10 q^{68} + 16 q^{70} + 9 q^{71} - 30 q^{72} - 57 q^{73} + 46 q^{74} + 26 q^{75} + 34 q^{76} + 2 q^{77} + 36 q^{78} - 7 q^{79} + q^{80} + 22 q^{81} - 25 q^{82} - 15 q^{83} + 14 q^{84} - 30 q^{85} + 51 q^{86} - 37 q^{87} - 7 q^{88} + 78 q^{89} + 17 q^{90} - 31 q^{91} - 30 q^{92} - 43 q^{93} + 20 q^{94} + q^{95} + 6 q^{96} - 38 q^{97} + 2 q^{98} + 2 q^{99}+O(q^{100}) \) 34 * q - 34 * q^2 - 6 * q^3 + 34 * q^4 + q^5 + 6 * q^6 - 22 * q^7 - 34 * q^8 + 30 * q^9 - q^10 + 7 * q^11 - 6 * q^12 - 11 * q^13 + 22 * q^14 - 18 * q^15 + 34 * q^16 - 10 * q^17 - 30 * q^18 + 34 * q^19 + q^20 + 14 * q^21 - 7 * q^22 - 30 * q^23 + 6 * q^24 + 11 * q^25 + 11 * q^26 - 21 * q^27 - 22 * q^28 + 12 * q^29 + 18 * q^30 - 13 * q^31 - 34 * q^32 - 4 * q^33 + 10 * q^34 - 16 * q^35 + 30 * q^36 - 46 * q^37 - 34 * q^38 - 36 * q^39 - q^40 + 25 * q^41 - 14 * q^42 - 51 * q^43 + 7 * q^44 - 17 * q^45 + 30 * q^46 - 20 * q^47 - 6 * q^48 - 2 * q^49 - 11 * q^50 + 4 * q^51 - 11 * q^52 - 7 * q^53 + 21 * q^54 - 39 * q^55 + 22 * q^56 - 6 * q^57 - 12 * q^58 + 19 * q^59 - 18 * q^60 - 26 * q^61 + 13 * q^62 - 57 * q^63 + 34 * q^64 + 20 * q^65 + 4 * q^66 - 54 * q^67 - 10 * q^68 + 16 * q^70 + 9 * q^71 - 30 * q^72 - 57 * q^73 + 46 * q^74 + 26 * q^75 + 34 * q^76 + 2 * q^77 + 36 * q^78 - 7 * q^79 + q^80 + 22 * q^81 - 25 * q^82 - 15 * q^83 + 14 * q^84 - 30 * q^85 + 51 * q^86 - 37 * q^87 - 7 * q^88 + 78 * q^89 + 17 * q^90 - 31 * q^91 - 30 * q^92 - 43 * q^93 + 20 * q^94 + q^95 + 6 * q^96 - 38 * q^97 + 2 * q^98 + 2 * q^99

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